% 
% Written by:
% -- 
% John L. Weatherwax                2006-12-31
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

clc; 
close all; 

max_n_people_ahead = 50; 

% Compute the probability that we have identical birthdays among n people:
%
prob_n_nonmatching_bdays= [];
for n=1:max_n_people_ahead, 
  num = 365-(n-1);
  den = 365.;
  p   = num/den;
  if( n==1 )
    prob_n_nonmatching_bdays = 1.; 
  else
    prob_n_nonmatching_bdays = [ prob_n_nonmatching_bdays, prob_n_nonmatching_bdays(end) * p ];
  end
end 

prob_of_win = prob_n_nonmatching_bdays .* ( (1:max_n_people_ahead)/365 );

plot( 1:n, prob_of_win ); xlabel( 'number of people ahead in line' ); ylabel(' probability of winning a free ticket' ); 
saveas( gcf, 'prob_of_win_at_position_np1', 'epsc' ); 

% print the best spot 
[v,spot] = max( prob_of_win );
v
spot